Diamond is cut for use in ornamentation to obtain a brilliant diamond and accessory and there are the round brilliant cut ornamental diamond and accessory of a 58-faceted body.
Mathematician Tolkowsky proposed a cut believed to be ideal, as a design to enhance brilliance of the round brilliant cut ornamental diamond, which has the pavilion angle of 40.75°, the crown angle of 34.50°, and the table diameter of 53% of the girdle diameter. A design developed from it is one called the GIA (Gemological Institute of America) system.
The inventors conducted study on cuts to enhance brilliance of ornamental diamonds and proposed in Patent Document 1, the cut design wherein the pavilion angle p was between 45° and 37.5° both inclusive and the crown angle (c) fell within the range of −3.5×p+163.6≧c≧−3.8333×p+174.232, as one permitting a viewer who views a round brilliant cut diamond from above the table facet thereof, to simultaneously view light emerging from the crown facets after incidence into the crown facets, light emerging from the crown facets after incidence into the table facet, and light emerging from the table facet after incidence into the crown facets. In the cut design, the center value of the pavilion angle p is 38.5° and that of the crown angle (c) is 27.92°. Since the round brilliant cut diamonds are designed with emphasis on the brilliance of the crown facets as well as the brilliance of the table facet, the diameter of the table facet is from 40 to 60% of that of the girdle, and it is from 33 to 60% in the diamond proposed before by the inventors.
The brilliance of an ornamental diamond is sensed by a viewer in such a manner that light is incident from the outside into the diamond and the incident light is reflected inside the diamond to reach the viewer. The degree of brilliance of a diamond is determined by a quantity of the reflected light from the diamond. The quantity of reflected light is usually evaluated by a physical quantity of reflected light.
The human perception, however, is not determined by the physical quantity of reflected light only. For letting a viewer sense beauty of a diamond, the diamond needs to provide a large quantity of light to be sensed by the viewer, i.e., a large quantity of physiologically or psychologically visually-perceived reflected light. There are the Fechner's law and Stevens' law as to the quantity of light perceived by humans (cf. Non-patent Document 1). The Fechner's law states that the quantity of visually-perceived light is the logarithm of the physical quantity of light. When the Stevens' law is applied on the assumption that a light source is a point light source, the quantity of visually-perceived light is the square root of the physical quantity of light. Based on either of the Fechner's and Stevens' laws, many conclusions are considered to be substantially identical without significant error though they are quantitatively different. Then the inventors adopted the Stevens' law to evaluate the quantity of reflected light from the diamond and thereby to determine the quantity of visually-perceived light, and evaluated the brilliance of diamond, based on the quantity of visually-perceived reflected light in the case of the visually-perceived light being the reflected light. We proposed in Patent Document 2 that the quantity of reflected light from the diamond, though it must be different depending upon illumination conditions, was to be evaluated in such a practical condition that incident light to be blocked by the viewer and incident light coming from sufficiently far distances were excluded from incident light from a planar light source with uniform luminance and the quantity of effective visually-perceived reflected light was evaluated using reflection of the remaining incident light, and also proposed a design of brilliant cut diamond capable of increasing the quantity of effective visually-perceived reflected light.
Patent Document 1: Japanese Patent No. 3,643,541
Patent Document 2: Japanese Patent Application Laid-open No. 2003-310318
Non-patent Document 1: “Shichikaku” 2000, pp 10-12, authored by Takao Matsuda and published by BAIFUKAN CO., LTD